H2O + I2 + PH3 = HI + H3PO2

H_2O water + I_2 iodine + PH_3 phosphine ⟶ HI hydrogen iodide + H3PO2

Balance the chemical equation algebraically: H_2O + I_2 + PH_3 ⟶ HI + H3PO2 Add stoichiometric coefficients, c_i, to the reactants and products: c_1 H_2O + c_2 I_2 + c_3 PH_3 ⟶ c_4 HI + c_5 H3PO2 Set the number of atoms in the reactants equal to the number of atoms in the products for H, O, I and P: H: | 2 c_1 + 3 c_3 = c_4 + 3 c_5 O: | c_1 = 2 c_5 I: | 2 c_2 = c_4 P: | c_3 = c_5 Since the coefficients are relative quantities and underdetermined, choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, set c_3 = 1 and solve the system of equations for the remaining coefficients: c_1 = 2 c_2 = 2 c_3 = 1 c_4 = 4 c_5 = 1 Substitute the coefficients into the chemical reaction to obtain the balanced equation: Answer: | | 2 H_2O + 2 I_2 + PH_3 ⟶ 4 HI + H3PO2

+ + ⟶ + H3PO2

water + iodine + phosphine ⟶ hydrogen iodide + H3PO2

Construct the equilibrium constant, K, expression for: H_2O + I_2 + PH_3 ⟶ HI + H3PO2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the activity expression for each chemical species. • Use the activity expressions to build the equilibrium constant expression. Write the balanced chemical equation: 2 H_2O + 2 I_2 + PH_3 ⟶ 4 HI + H3PO2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 2 | -2 I_2 | 2 | -2 PH_3 | 1 | -1 HI | 4 | 4 H3PO2 | 1 | 1 Assemble the activity expressions accounting for the state of matter and ν_i: chemical species | c_i | ν_i | activity expression H_2O | 2 | -2 | ([H2O])^(-2) I_2 | 2 | -2 | ([I2])^(-2) PH_3 | 1 | -1 | ([PH3])^(-1) HI | 4 | 4 | ([HI])^4 H3PO2 | 1 | 1 | [H3PO2] The equilibrium constant symbol in the concentration basis is: K_c Mulitply the activity expressions to arrive at the K_c expression: Answer: | | K_c = ([H2O])^(-2) ([I2])^(-2) ([PH3])^(-1) ([HI])^4 [H3PO2] = (([HI])^4 [H3PO2])/(([H2O])^2 ([I2])^2 [PH3])

Construct the rate of reaction expression for: H_2O + I_2 + PH_3 ⟶ HI + H3PO2 Plan: • Balance the chemical equation. • Determine the stoichiometric numbers. • Assemble the rate term for each chemical species. • Write the rate of reaction expression. Write the balanced chemical equation: 2 H_2O + 2 I_2 + PH_3 ⟶ 4 HI + H3PO2 Assign stoichiometric numbers, ν_i, using the stoichiometric coefficients, c_i, from the balanced chemical equation in the following manner: ν_i = -c_i for reactants and ν_i = c_i for products: chemical species | c_i | ν_i H_2O | 2 | -2 I_2 | 2 | -2 PH_3 | 1 | -1 HI | 4 | 4 H3PO2 | 1 | 1 The rate term for each chemical species, B_i, is 1/ν_i(Δ[B_i])/(Δt) where [B_i] is the amount concentration and t is time: chemical species | c_i | ν_i | rate term H_2O | 2 | -2 | -1/2 (Δ[H2O])/(Δt) I_2 | 2 | -2 | -1/2 (Δ[I2])/(Δt) PH_3 | 1 | -1 | -(Δ[PH3])/(Δt) HI | 4 | 4 | 1/4 (Δ[HI])/(Δt) H3PO2 | 1 | 1 | (Δ[H3PO2])/(Δt) (for infinitesimal rate of change, replace Δ with d) Set the rate terms equal to each other to arrive at the rate expression: Answer: | | rate = -1/2 (Δ[H2O])/(Δt) = -1/2 (Δ[I2])/(Δt) = -(Δ[PH3])/(Δt) = 1/4 (Δ[HI])/(Δt) = (Δ[H3PO2])/(Δt) (assuming constant volume and no accumulation of intermediates or side products)

| water | iodine | phosphine | hydrogen iodide | H3PO2 formula | H_2O | I_2 | PH_3 | HI | H3PO2 Hill formula | H_2O | I_2 | H_3P | HI | H3O2P name | water | iodine | phosphine | hydrogen iodide | IUPAC name | water | molecular iodine | phosphine | hydrogen iodide |

| water | iodine | phosphine | hydrogen iodide | H3PO2 molar mass | 18.015 g/mol | 253.80894 g/mol | 33.998 g/mol | 127.912 g/mol | 65.996 g/mol phase | liquid (at STP) | solid (at STP) | gas (at STP) | gas (at STP) | melting point | 0 °C | 113 °C | -132.8 °C | -50.76 °C | boiling point | 99.9839 °C | 184 °C | -87.5 °C | -35.55 °C | density | 1 g/cm^3 | 4.94 g/cm^3 | 0.00139 g/cm^3 (at 25 °C) | 0.005228 g/cm^3 (at 25 °C) | solubility in water | | | slightly soluble | very soluble | surface tension | 0.0728 N/m | | | | dynamic viscosity | 8.9×10^-4 Pa s (at 25 °C) | 0.00227 Pa s (at 116 °C) | 1.1×10^-5 Pa s (at 0 °C) | 0.001321 Pa s (at -39 °C) | odor | odorless | | | |